Q. What exactly does it mean 4/11?
 
A. In a nutshell, the first value (X in X/Y) is the brute force search depth -- all moves up to depth X have been searched.
 
The second value is the minimum extension depth (Johan calls it the "nominal depth"). Note the word "minimum", which is why The King can announce Mate in 10 (19 plies deep) at depth 1/9, as it does in this position:
 
[D]4r1k1/qp1r1p2/2pb1Bp1/p6p/2PP1n1R/1P3P2/P4P2/2Q2K1R w - - 0 1
 
Time Depth Score Positions Moves
0:00 1/3 -1.80 2438 1.Rxf4 Bxf4 2.Qxf4 Re6 3.Be5 b6
0:00 1/4 -1.26 7609 1.Rxf4 Bxf4 2.Qxf4 Re6 3.Be5 Kh7
 4.Qg5
0:00 1/5 -1.26 24204 1.Rxf4 Bxf4 2.Qxf4 Re6 3.Be5 Kh7
 4.Qg5
0:01 1/6 -1.43 107926 1.Rxf4 Re6 2.Rf5 Rxf6 3.Rxf6 Qxd4
 4.Qg5 Be5
0:02 1/6 1.34 140417 1.Rxh5 gxh5 2.Qxf4 Re1+ 3.Kxe1
 Re7+ 4.Be5 Bxe5 5.Qg5+ Kf8 6.dxe5
0:03 1/7 2.28 201244 1.Rxh5 gxh5 2.Qxf4 Re1+ 3.Kxe1
 Re7+ 4.Be5 Bxe5 5.dxe5 Rd7 6.Qg5+
 Kf8 7.Rxh5
0:10 1/8 9.09 708832 1.Rxh5 gxh5 2.Qxf4 Re1+ 3.Kxe1
 Re7+ 4.Kf1 Re1+ 5.Kxe1 Bb4+ 6.Kf1
 Kf8 7.Rxh5
0:14 1/8 13.43 1017822 1.Qxf4 Re1+ 2.Kxe1 Bxf4 3.Rxh5
 Re7+ 4.Kf1 Re1+ 5.Kxe1 Bd2+ 6.Kxd2
 gxh5 7.Rxh5 Qxd4+ 8.Bxd4 Kf8 9.Rxa5
 Ke7
0:21 1/9 Mate10 1755749 1.Qxf4 Re1+ 2.Kg2 Rg1+ 3.Kxg1 Qc5
 4.Rxh5 gxh5 5.Qh6 Qg5+ 6.Qxg5+
 Kf8 7.Qg8+ Kxg8 8.Rxh5 Bh2+ 9.Rxh2
 Kf8 10.Rh8#
0:22 1/10 Mate10 1855049 1.Qxf4 Re1+ 2.Kg2 Rg1+ 3.Kxg1 Qc5
 4.Rxh5 gxh5 5.Qh6 Qg5+ 6.Qxg5+
 Kf8 7.Qg8+ Kxg8 8.Rxh5 Bh2+ 9.Rxh2
 Kf8 10.Rh8#

References

https://www.stmintz.com/ccc/index.php?id=249630